Since originally writing this post, Evoto has come along and done just that: Letting you base all your shots on the crop of a single one. Works perfectly. In fact, if you're doing headshots or portraits, there's no need to open Lightroom at all. Evoto can shoot tethered, do a quick retouch on the fly (as the photo appears), and export. I'm not affiliated in any way with them, just impressed with how good they've gotten so quickly! Highly recommend.
Evoto is great, but for me that do school portraits I have to export the same picture in more formats and I use all keywords, face detection and color grading on the Lightroom. I don't do any massive edition beside that.